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August 1st, 2008, 12:13 PM   #1
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Need Help Quick!

This is a problem I'm stuck on.

You've measured the mass of some pennies that were minted before 1982, when they had a different composition than they do today. They were still made of zinc and copper, but in a different ratio. You've found that one penny has a mass of 3.1, and has a volume of 0.35 cubic centimeters. Find the mass of the copper in this penny.

Density of Zinc=7.13 grams of mass per cubic centimeter of volume.
Density of Copper=8.96 grams of mass per cubic centimeter of volume.

Please help, I'm a math n00b.
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August 1st, 2008, 12:24 PM   #2
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Re: Need Help Quick!

Well okay, this sounds like problem for...linear algebra! So, do a little pre-calculation to find the density of the penny in grams per cubic centimeter. Lets call the fraction of the penny made from copper c and from zinc z. Now there are two pieces of information we have:

1) The sum of c and z must be 1. Why?

2) If you take c and z for weights to find the weighted average of the densities of copper and zinc this should equal the density of the penny.

See what you can do in the way of setting up those equations. Then you will be looking at a system of two equations with two unknowns, hopefully something you have had experience with, but if you haven't that will just make it more fun!
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August 1st, 2008, 12:29 PM   #3
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Re: Need Help Quick!

Sorry but I'm still very confused with the problem
Could you get a little more in depth with what I should do next?
If you could solve the problem with work shown, that would be terrific!
Thank you very much
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August 1st, 2008, 12:38 PM   #4
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Re: Need Help Quick!

Are you supposed to be solving this using systems of linear equations? Have you seen things that look like this:

x + 2y = 3
2x + 2y = 4

If you have, let me start you out with the first line of the system you should be looking at:

c + z = 1

Remember, c is the portion the the penny made of copper (as a decimal) and z is the portion of the penny made of zinc (as a decimal). This is why you want c+z=1. You couldn't have a penny that was 50% copper and 90% zinc.
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August 1st, 2008, 12:46 PM   #5
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Re: Need Help Quick!

Ok....So would it be easiest to find the total mass in the penny and subtract the mass of zinc? How would we do this?
If that's not the right path then enlighten me.
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August 1st, 2008, 02:14 PM   #6
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Re: Need Help Quick!

Okay, try to put this statement into an equation:

The density of copper times the percent copper plus the density of zinc times the percent zinc is the density of the penny.
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August 1st, 2008, 04:08 PM   #7
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Re: Need Help Quick!

Mass of copper = c
Mass of zinc = Z

1. c + z = 3.1

Volume = mass/density

Volume of copper = c/8.96
Volume of zinc = z/7.13

2. c/8.96 + z/7.13 = 0.35

Solve equations 1 and 2 for c and z.
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August 22nd, 2008, 11:10 AM   #8
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Re: Need Help Quick!

now that i have all of the needed information, could you please tell me where to start?
How do I get the answer for C and Z?
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August 22nd, 2008, 11:40 AM   #9
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You were originally asked to find c, so you need to eliminate z from the equations.

Since c + z = 3.1, z = 3.1 - c.

Using this result to replace z with 3.1 - c in the second equation gives c/8.96 + (3.1 - c)/7.13 = 0.35.

Rearranging that a bit gives c(1/8.96 - 1/7.13) = 0.35 - 3.1/7.13,
so c = (0.35 - 3.1/7.13)/(1/8.96 - 1/7.13)
       = 2.96 approximately.

Now design a new problem! If you can't do that, realize that you won't learn much by simply reading one solution; you need to explore and investigate for yourself.
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